A Critical Analysis of One-Loop Neutrino Mass Models with Minimal Dark Matter

TL;DR

This paper critically examines minimal one-loop neutrino mass models with dark matter candidates, revealing fundamental symmetry-breaking issues that prevent their viability, and concludes that such minimal models are not feasible.

Contribution

The paper demonstrates that minimal one-loop R$ u$MDM models cannot produce stable dark matter due to explicit symmetry-breaking problems, establishing a no-go result for these models.

Findings

Minimal one-loop R$ u$MDM models lack accidental symmetry for dark matter stability.

Explicit symmetry-breaking terms render the dark matter candidate unstable.

No viable minimal one-loop neutrino mass models with stable dark matter exist under current frameworks.

Abstract

A recent paper investigated minimal R$\nu$MDM models with the type T1-iii and T3 one-loop topologies. However, the candidate most-minimal model does not possess an accidental symmetry - the scalar potential contains an explicit symmetry breaking term, rendering the dark matter unstable. We present two models that cure this problem. However, we further show that all of the proposed minimal one-loop R$\nu$MDM models suffer from a second problem - an additional source of explicit $Z_2$ symmetry breaking in the Yukawa sector. We perform a more-general analysis to show that neutrino mass models using either the type T3 or type T1-iii one-loop topologies do not give viable minimal dark matter candidates. Consequently, one-loop models of neutrino mass with minimal dark matter do not appear possible. Thus, presently there remains a single known (three-loop) model of neutrino mass that gives stable dark matter without invoking any new symmetries.